UPDATE 1-Obama, Clinton all smiles in joint interview

(Recasts with comments from interview)

WASHINGTON, Jan 25 (Reuters) - Bitter rivals in the 2008 presidential campaign, President Barack Obama and Secretary of State Hillary Clinton kept smiling at each other in a joint interview to CBS that Clinton said would have seemed "improbable" years ago.

"It has been a great collaboration over the last four years. I'm going to miss her," Obama said in a televised excerpt from the CBS "60 Minutes" program that will air on Sunday.

The interview, conducted at the White House on Friday, comes as Clinton prepares to step down and the Senate confirmation process moves forward for Senator John Kerry, Obama's pick to replace her.

"A few years ago it would have been seen as improbable (to have a joint interview) because we had that very long, hard primary campaign," Clinton said in the excerpt.

"And then President Obama asked me to be secretary of state and I said yes. And why did he ask me and why did I say yes? Because we both love our country."

Clinton this week forcefully defended her handling of the deadly September attack on the U.S. diplomatic mission in the Libyan city of Benghazi and denied any effort to mislead the American people.

There is widespread speculation about whether Clinton, who leaves with high public approval ratings after serving from the start of Obama's first term, will make another White House run in 2016.

"There are not a lot of people in the world who go through what they do," Philippe Reines, deputy assistant secretary of state and Clinton aide, told CNN about the relationship between Clinton and Obama. "For good or bad, (they've) been put together."

The interview, which will be broadcast at 7 p.m. EST (0000 Monday GMT), is Obama's first since his ceremonial inauguration on Monday. It is also the first time that he and Clinton have been interviewed together. (Reporting By Matt Spetalnick, additional reporting by Anna Yukhananov; Editing by Vicki Allen and Xavier Briand)